The Saints boss has been impressed by the 26-year-old's performances since his appointment in January and revealed that contract talks will begin in the coming weeks
The 26-year-old has been one of Saints' stand-out performers upon their return to the Premier League, having scored four goals in 26 appearances so far.
And Pochettino, who arrived at the club to replace Nigel Adkins in January, has been impressed with the winger's contributions during his short time in charge.
"In the coming weeks we will be speaking at a club level with the appropriate people to decide on the matters of players at the club,” he told reporters through an interpreter.
"I myself haven't spoken anything about his contract. I've only recently arrived so my first priority has to be the whole of the team, not just one player. There are certain movements that were already happening with players when I arrived.
"Puncheon is a player I am counting on and he is a player that has certain qualities and skills that are good for the team so, yes, I'd like him to stay."
Despite Southampton sitting 13 points short of the 40-point mark normally associated with survival, the Argentine has already stated his intention to bring in new players in the summer.
He continued: "I always think that in football it is not just one person signing any players, it is the club signing the players.
"Now I am the manager here and I will probably bring in some players.
"Some players will work out so maybe sometime in the future I may be thanked, but then there will be players that didn't work out. That is how football really is."